Jveiguela, There is one thing you need to understand! You can count on a $1000 premium on the price of any equal quality double rifle if it is chambered for 470NE, over just about any other chambering. The cartridge isn't worth the premium, ballisticly! Many others will do anything just as well as the 470NE, with a $1000 discount in price!

IMO, you will be lucky to find an odd chambering in a black powder double rifle for your very conservative price range.
That doesn't mean you wont find a bargain, stranger things have happened!

Some one suggested you could maybe find one cheaper in one of the .400 calibers. That may be so with some of the odd balls, but a 450/400 3" will again cost you a primium, over others of like size.

I think if your heart is set on a 470NE, then I'd buy a new Searcy at $9500, or a Merkel at about the same price new, though list is $10,595 for a new Merkel, they can be found at lower price. Used the Merkel will set you back around $8500 if it is like new. My money would be on haveing Butch Searcy build me a PH model to order for $9500.

If you can live with the cocking system, one can pick up a Krieghoff double at a real reasonable price used, but even then you are looking at $7K, to 8K for one in 470NE. Like you I wish I could find a few double rifles in the $3K-5K range, if I did, I'd refinance the house, and car to get the money!